We want to find a scalar function
such that
.
So we need to have
Integrating both sides with respect to
gives
Differentiating with respect to
gives
So we find that
By the fundamental theorem of calculus, we then know the line integral depends only on the values of
at the endpoints of the path. Therefore
The correct answer is C
Sigma Notation is when we take all of the whole numbers between the starting point (which can be found as the number under the sigma sign) and the end number (which can be found above the sigma sign). Therefore, we will add together all of the values of 3k + 2 for when k is equal to all of the numbers between 2 and 7. So, let's evaluate each one first.
When k = 2
3(2) + 2 = 8
When k = 3
3(3) + 2 = 11
When k = 4
3(4) + 2 = 14
When k = 5
3(5) + 2 = 17
When k = 6
3(6) + 2 = 20
When k = 7
3(7) + 2 = 23
So we know we have the following.
8 + 11 + 14 + 17 + 20 + 23
Now for the number after the comma, we are just looking for the answer of them all added together. So the final answer should be
8 + 11 + 14 + 17 + 20 + 23, 93
<span>1 7/8 x 2 1/3
= 15/8 x 7/3
= 35/8
= 4 3/8
hope it helps</span>
Answer: "
-2y³ + 3y²<span>
+ 27y " .
_______________________________________________________Refer to the completed chart below (image attached).</span>
_______________________________________________________Using the completed chart below (image attached), we can write out the terms:
__________________________________________________ y³ − 3y³ + 9y² + 3y² − 9y² + 27y ;
Then, we can combine the "like terms" ;
__________________________________________y³ − 3y³ = -2y³ ;
+9y² + 3y² − 9y² = + 3y² ;
___________________________________________________________to get: -2y³ + 3y² ; and bring down the "+27y" ;
___________________________________________________________ Answer: "
-2y³ + 3y²<span>
+ 27y " . </span>Refer to chart below (image attached).
___________________________________________________________
% means 'parts out of 100' so
25%=25/100
is 12 is 25 parts out of 100 of a number
so 12=(25/100)x
25/100 simplifies to 1/4
or if 12=(1/4)x
we multiply both sides by 4 and get
48=1x
